Before TVs were invented, we had actual films being rotated by hand crank or by a motor - their fps is independent of electrical mains. But cathode ray tube TVs were made to match mains frequency. Then to avoid having to do some kind of conversion, it was easier to film your movies to match TVs.
I think 24 fps for sound film originally arose from the requirements of the optical soundtrack: slower running 35mm film wouldn't have enough resolution for decent sound quality. That's my guess anyway.
Silent films were often shot on slower rates around 16-18 fps (which explains the widespread comic "speed-up" look for video copies of silent movies, as the transfer was done the easy way by playing it back at 24).
There are tricks you can do with shutter angle that negate this, but they are beyond the scope of this comment.